Fast matrix computations for pair-wise and column-wise commute times and Katz scores

We first explore methods for approximating the commute time and Katz score between a pair of nodes. These methods are based on the approach of matrices, moments, and quadrature developed in the numerical linear algebra community. They rely on the Lanczos process and provide upper and lower bounds on an estimate of the pair-wise scores. We also explore methods to approximate the commute times and Katz scores from a node to all other nodes in the graph. Here, our approach for the commute times is based on a variation of the conjugate gradient algorithm, and it provides an estimate of all the diagonals of the inverse of a matrix. Our technique for the Katz scores is based on exploiting an empirical localization property of the Katz matrix. We adopt algorithms used for personalized PageRank computing to these Katz scores and theoretically show that this approach is convergent. We evaluate these methods on 17 real world graphs ranging in size from 1000 to 1,000,000 nodes. Our results show that our pair-wise commute time method and column-wise Katz algorithm both have attractive theoretical properties and empirical performance.Comment: 35 pages, journal version of http://dx.doi.org/10.1007/978-3-642-18009-5_13 which has been submitted for publication. Please see http://www.cs.purdue.edu/homes/dgleich/publications/2011/codes/fast-katz/ for supplemental code

Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB

In this article, we develop a simple mathematical GNU Octave/MATLAB code that is easy to modify for the simulation of mathematical models governed by fractional-order differential equations, and for the resolution of fractional-order optimal control problems through Pontryagin's maximum principle (indirect approach to optimal control). For this purpose, a fractional-order model for the respiratory syncytial virus (RSV) infection is considered. The model is an improvement of one first proposed by the authors in [Chaos Solitons Fractals 117 (2018), 142--149]. The initial value problem associated with the RSV infection fractional model is numerically solved using Garrapa's fde12 solver and two simple methods coded here in Octave/MATLAB: the fractional forward {Euler's} method and the predict-evaluate-correct-evaluate (PECE) method of Adams--Bashforth--Moulton. A fractional optimal control problem is then formulated having treatment as the control. The fractional Pontryagin maximum principle is used to characterize the fractional optimal control and the extremals of the problem are determined numerically through the implementation of the forward-backward PECE method. The implemented algorithms are available on GitHub and, at the end of the paper, in appendixes, both for the uncontrolled initial value problem as well as for the fractional optimal control problem, using the free GNU Octave computing software and assuring compatibility with MATLAB. The developed Octave/Matlab code is available at [https://github.com/SilverioRosa/numres-focp]This research was funded by The Portuguese Foundation for Science and Technology (FCT—Fundação para a Ciência e a Tecnologia), grants number UIDB/50008/2020 (S.R.) and UIDB/04106/2020 (D.F.M.T.).publishe

Calibration and application of a B-dot sensor to study the initiation of vacuum surface flashover

\u27Calibration\u27, as the name suggests is the act of checking or adjusting the accuracy of a measuring instrument by comparison with a standard. Two techniques, the equal length test and the short circuit test, have been developed to determine the characteristic impedance and propagation coefficient of a single lossy transmission line and a lossy transmission line network in cascade based solely on the input reflection coefficient S-parameter, S11, VNA measurements over a wide bandwidth of frequencies. For the transmission line network case, the characteristic impedance and propagation coefficient for each line in the cascade, excluding the last line, are known. Theoretical expressions needed for interpreting VNA measured data have been developed. A wideband, coaxial cable calibration test stand is characterized based on the novel equal length technique. The test stand is used to calibrate a B-dot in the frequency domain to obtain its response function. To verify the calibration process, the calibrated B-dot will be used to measure the surface current density on a radial transmission driven by a pulsed power source. These results will be compared against simulation using a Graphical Large Scale Plasma (GLSP) code. This calibrated B-dot will be used in future surface breakdown pulse power experiments on plastics measuring fast sub-nanosecond rise time phenomena

Secured Energy Optimization in Mobile Ad Hoc Networks

Due to limited resources, it is essential to optimize energy consumption in mobile ad hoc networks. There exist different ways to optimize energy usage for mobile ad hoc network. Our thesis proposes usage of secured mobile dominating sets for efficient optimized use of energy in a mobile ad hoc network. Existing approaches for energy optimization use different techniques. Some of them include techniques such as dominating sets, communication reduction between nodes and concept of balanced forces. Energy optimization in dominating set based approaches is carried out by the use of some special nodes, which are the only working nodes in the network. The dominating set based approach can be modified to improve network life by improving energy consumption per node. Further more these approaches do not provide security. In this thesis we propose the concept of mobile dominating set, which updates the dominating set nodes at regular intervals based on the nodes mobility and the network topology constraints. This further improves the network life by utilizing the maximum energy per node. Furthermore, we propose a secure dominating set mechanism, which provides security with minimum energy expenditure for mobile dominating sets. Our approach starts by constructing the dominating set based on the initial composition between two networks, security key network and mobile ad hoc network, and then depending on the nodes mobility, decrease in energy levels of dominating set nodes, network topology constraints; it recalculates the dominating set with new mobile network links to include secured communication between the dominating set nodes. The results are compared with unsecured dominating set networks, secured mobile ad hoc networks and general mobile ad hoc networks. The results show that the energy consumed for each network in increasing order as unsecured dominating set networks, secured dominating set networks, general mobile ad hoc networks and secured mobile ad hoc networks. It also shows that the narrow difference in energy levels for unsecured dominating set network and secured dominating set network decreases as the network size increases. It also shows that there is very small difference of average path lengths between secured dominating set network and unsecured dominating set network. The results also show that the number of nodes survived decreases as the network period increases with improved network life per each node.Computer Science Departmen

A Framework for Certified Self-Stabilization

We propose a general framework to build certified proofs of distributed self-stabilizing algorithms with the proof assistant Coq. We first define in Coq the locally shared memory model with composite atomicity, the most commonly used model in the self-stabilizing area. We then validate our framework by certifying a non trivial part of an existing silent self-stabilizing algorithm which builds a $k$-hop dominating set of the network. We also certified a quantitative property related to the output of this algorithm. Precisely, we show that the computed $k$-hop dominating set contains at most $\lfloor \frac{n-1}{k+1} \rfloor + 1$ nodes, where $n$ is the number of nodes in the network. To obtain these results, we also developed a library which contains general tools related to potential functions and cardinality of sets

New VLSI design of a MAP/BCJR decoder.

Any communication channel suffers from different kinds of noises. By employing forward error correction (FEC) techniques, the reliability of the communication channel can be increased. One of the emerging FEC methods is turbo coding (iterative coding), which employs soft input soft output (SISO) decoding algorithms like maximum a posteriori (MAP) algorithm in its constituent decoders. In this thesis we introduce a design with lower complexity and less than 0.1dB performance loss compare to the best performance observed in Max-Log-MAP algorithm. A parallel and pipeline design of a MAP decoder suitable for ASIC (Application Specific Integrated Circuits) is used to increase the throughput of the chip. The branch metric calculation unit is studied in detail and a new design with lower complexity is proposed. The design is also flexible to communication block sizes, which makes it ideal for variable frame length communication systems. A new even-spaced quantization technique for the proposed MAP decoder is utilized. Normalization techniques are studied and a suitable technique for the Max-Log-MAP decoder is explained. The decoder chip is synthesized and implemented in a 0.18 mum six-layer metal CMOS technology. (Abstract shortened by UMI.)Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .S23. Source: Masters Abstracts International, Volume: 43-05, page: 1783. Adviser: Majid Ahmadi. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004

A New Simplified Algorithm Suitable for Implementation on FPGA for Turbo Codes

In this thesis, a new algorithm for Turbo codes and a novel implementation of turbo decoder employed with this algorithm is developed. The decoder has an optimal performance in terms of Bit Error Rate(BER) in all Signal to Noise Ratio(SNR) for all frame sizes and any states of Turbo codes. In hardware implementation, we combine the normalization and matrices modules in a single module in order to minimize the internal connection delay which is the bottleneck in hardware implementation, so that the result can be obtained in one single clock signal. Having implemented in this fashion, data rate of 28Mbps for16 state decoder has been achieved. This can be further improved by changing the algorithm for the normalization modules and LLR modules with MAX operator. The matrices modules with the proposed algorithm and the normalization and LLR modules with MAX-LOG-MAP algorithm have been implemented to achieve a data rate of 60Mbps

On the application of extreme-value statistics to command oriented problems

Extreme value theory for estimating statistical parameters of spacecraft communication system